The hybrid finite/discrete element method in description of macrostructural behavior of salt rocks

The correct prediction and assessment of the surrounding rock mass behavior around construction objects in salt rocks requires a clear understanding of long-term deformation processes in these rocks when subjected to different stress and temperature impacts. This article presents the analysis of the mechanical properties and mechanical behavior of salts. Furthermore, the mathematical descriptions and numerical modeling of the salt rock behavior are addressed. The article proposes an approach to modeling the mechanical behavior of polycrystal materials (including salt rocks) with regard to their macrostructural characteristics. The approach uses the Voronoi Tessellation as the polycrystal macrostructure description and the hybrid finite/discrete element method of deformation and fracture modeling. The scope of the studies embraced various factors of influence on the shape of the deformation curve in the uniaxial compression tests with the preset displacements. The resultant numerical model is usable for the stress–strain analysis of rock mass and for the location of possible failure sites. The further improvement of the deformation model will include the microlevel rheology and application of the model in stability prediction in largeand small-diameter holes and other small objects.

Karasev M. A., Petrushin V. V., Rysin A. I. The hybrid finite/discrete element method in description of macrostructural behavior of salt rocks. MIAB. Mining Inf. Anal. Bull. 2023;(4):48-66. [In Russ]. DOI: 10.25018/0236_1493_2023_4_0_48.

M.A. Karasev¹, Dr. Sci. (Eng.), Assistant Professor, e-mail: karasevma@gmail.com, ORCID ID: 0000-0001-8939-0807,
V.V. Petrushin¹, Graduate Student, e-mail: vlad.petrushin.93@mail.ru, ORCID ID: 0000-0001-7743-864X,
A.I. Rysin, Head of Laboratory, «EuroChem-Project» Ltd, Saint-Petersburg, 199106, Russia,
¹ Saint-Petersburg Mining University, 199106, Saint-Petersburg, Russia.

V.V. Petrushin, e-mail: vlad.petrushin.93@mail.ru.

1. Liu W., Zhang Z., Chen J., Fan J., Jiang D., Jjk D., Li Y. Physical simulation of construction and control of two butted-well horizontal cavern energy storage using large molded rock salt specimens. Energy. 2019, vol. 185, pp. 682—694. DOI: 10.1016/j.energy.2019.07.014.

2. Gasumov R., Gasumov E., Minchenko Y. Features of the underground storages construction in depleted oil and gas condensate fields. Journal of Mining Institute. 2020, vol. 244, pp. 418—427. [In Russ]. DOI: 10.31897/pmi.2020.4.4.

3. Bérest P., Brouard B., Djakeun-Djizanne H., Hévin G. Thermomechanical effects of a rapid depressurization in a gas cavern. Acta Geotechnica. 2014, vol. 9, no. 1, pp. 181—186. DOI: 10.1007/s11440-013-0233-8.

4. Kuranov A. D., Bagautdinov I. I., Kotikov D. A., Zuev B. Yu. Integrated approach to safety pillar stability in slice mining in the Yakovlevo deposit. Gornyi Zhurnal. 2020, no. 1, pp. 115. [In Russ]. DOI: 10.17580/gzh.2020.01.23.

5. Yang C., Wang T., Li J., Ma H., Shi X., Daemen J. J. K. Feasibility analysis of using closely spaced caverns in bedded rock salt for underground gas storage: a case study. Environmental Earth Sciences. 2016, vol. 75, no. 15, pp. 1—15. DOI: 10.1007/s12665-016-5944-3.

6. Rybak Ya., Khayrutdinov M. M., Kuziev D. A., Kongar-Syuryun Ch. B., Babyr' N. V.Prediction of the geomechanical state of the rock mass when mining salt deposits with stowing. Journal of Mining Institute. 2022, vol. 253, pp. 61—70. [In Russ]. DOI: 10.31897/ PMI.2022.2.

7. Senseny P. E., Hansen F. D., Russell J. E., Carter N. L., Handin J. W. Mechanical behaviour of rock salt: phenomenology and micromechanisms. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts. 1992, vol. 29, no. 4, pp. 363—378. DOI: 10.1016/0148-9062(92)90513-Y.

8. Sriapai T., Walsri C., Fuenkajorn K. True-triaxial compressive strength of Maha Sarakham salt. International Journal of Rock Mechanics and Mining Sciences. 2013, vol. 61, pp. 256—265. DOI: 10.1016/j.ijrmms.2013.03.010.

9. Cristescu N., Hunsche U. Time effects in rock mechanics. New York, Wiley, 1998, 350 p.

10. Alkan H., Cinar Y., Pusch G. Rock salt dilatancy boundary from combined acoustic emission and triaxial compression tests. International Journal of Rock Mechanics and Mining Sciences. 2007, vol. 44, no. 1, pp. 108—119. DOI: 10.1016/j.ijrmms.2006.05.003.

11. Hunsche U. E. True triaxial failure tests on cubic rock salt samples. experimental methods and results. Finite Inelastic Deformations—Theory and Applications. Springer, Berlin, Heidelberg, 1992, pp. 525—536.

12. Van Sambeek L. L., Ratigan J. L., Hansen F. D. Dilatancy of rock salt in laboratory tests. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts. 1993, vol. 30, no. 7, pp. 735—738. DOI: 10.1016/0148-9062(93)90015-6.

13. DeVries K. L., Mellegard K. D., Callahan G. D. Salt damage criterion proof-of-concept research technical progress report for the reporting priod from October 1, 2000, through September 30. Respec, Rapid City, South Dakota, US. 2002.

14. Hunsche U., Hampel A. Rock salt—the mechanical properties of the host rock material for a radioactive waste repository. Engineering Geology. 1999, vol. 52, no. 3-4, pp. 271—291. DOI: 10.1016/ S0013-7952(99)00011-3.

15. Protosenya A. G., Katerov A. M. Development of stress and strain state of combined support for a vertical shaft driven in salt massif. MIAB. Mining Inf. Anal. Bull. 2022, no. 6-1, pp. 100—113. [In Russ]. DOI: 10.25018/0236_1493_2022_61_0_100.

16. Hunsche U., Schulze O. Das Kriechverhalten von Steinsalz. Kali und Steinsalz. 1994, vol. 11, no. 8/9, pp. 238—255.

17. Heusermann S., Rolfs O., Schmidt U. Nonlinear finite-element analysis of solution mined storage caverns in rock salt using the LUBBY2 constitutive model. Computers & Structures. 2003, vol. 81, no. 8—11, pp. 629—638. DOI: 10.1016/ S0045-7949(02)00415-7.

18. Weidinger P., Hampel A., Blum W., Hunsche U. Creep behaviour of natural rock salt and its description with the composite model. Materials Science and Engineering: A. 1997, vol. 234—236, pp. 646—648. DOI: 10.1016/ S0921-5093(97)00316-X.

19. Sedláček R., Blum W. Microstructure-based constitutive law of plastic deformation. Computational Materials Science. 2002, vol. 25, no. 1—2, pp. 200—206. DOI: 10.1016/ S0927-0256(02)00264-1.

20. Munson D. E. Constitutive model of creep in rock salt applied to underground room closure. International Journal of Rock Mechanics and Mining Sciences. 1997, vol. 34, no. 2, pp. 233—247. DOI: 10.1016/ S0148-9062(96)00047-2.

21. Aubertin M., Gill D. E., Ladanyi B. An internal variable model for the creep of rocksalt. Rock Mechanics and Rock Engineering. 1991, vol. 24, no. 2, pp. 81—97. DOI: 10.1007/ BF01032500.

22. Aubertin M., Julien M. R., Servant S., Gill D. E. A rate-dependent model for the ductile behavior of salt rocks. Canadian Geotechnical Journal. 1999, vol. 36, no. 4, pp. 660—674. DOI: 10.1139/t99-033.

23. Yahya O. M. L., Aubertin M., Julien M. R. A unified representation of the plasticity, creep and relaxation behavior of rocksalt. International Journal of Rock Mechanics and Mining Sciences. 2000, vol. 37, no. 5, pp. 787—800. DOI: 10.1016/ S1365-1609(00)00016-2.

24. Sun F., Meade E. D., O'Dowd N. P. Microscale modelling of the deformation of a martensitic steel using the Voronoi tessellation method. Journal of the Mechanics and Physics of Solids. 2018, vol. 113, pp. 35—55. DOI: 10.1016/j.jmps.2018.01.009.

25. Sun F., Meade E. D., O'Dowd N. P. Strain gradient crystal plasticity modelling of size effects in a hierarchical martensitic steel using the Voronoi tessellation method. International Journal of Plasticity. 2019, vol. 119, pp. 215—229. DOI: 10.1016/j.ijplas.2019.03.009.

26. Brückner-Foit A., Huang X. Numerical simulation of micro-crack initiation of martensitic steel under fatigue loading. International Journal of Fatigue. 2006, vol. 28, no. 9, pp. 963—971. DOI: 10.1016/j.ijfatigue.2005.08.011.

27. Müller C., Frühwirt T., Haase D., Schlegel R., Konietzky H. Modeling deformation and damage of rock salt using the discrete element method. International Journal of Rock Mechanics and Mining Sciences. 2018, vol. 103, pp. 230—241. DOI: 10.1016/j.ijrmms.2018.01.022.

28. Li H., Yang C., Ma H., Shi X., Zhang H., Dong Z. A 3D grain-based creep model (3DGBCM) for simulating long-term mechanical characteristic of rock salt. Journal of Petroleum Science and Engineering. 2020, vol. 185, article 106672. DOI: 10.1016/j.petrol.2019.106672.

29. Liang K., Xie L., He B., Zhao P., Zhang Y. Effects of grain size distributions on the macro-mechanical behavior of rock salt using micro-based multiscale methods. International Journal of Rock Mechanics and Mining Sciences. 2021, vol. 138, article 104592. DOI: 10.1016/j. ijrmms.2020.104592.

30. Protosenya A., Vilner M. Assessment of excavation intersections’ stability in jointed rock masses using the discontinuum approach. Rudarsko-Geološko-Naftni Zbornik. 2022, vol. 37, no. 2, pp. 137—147. DOI: 10.17794/rgn.2022.2.12.

31. Sinegubov V. Yu., Popov M. G., Vil'ner M. A., Sotnikov R. O. Influence of stoping on formation of damaged rock zones at boundaries of large cross-section excavations in apatite–nepheline mining. Gornyi Zhurnal. 2021, no. 8, pp. 26—30. [In Russ]. DOI: 10.17580/gzh.2021.08.04.

32. Cristescu N. D. Viscoplasticity of geomaterials. Visco-Plastic Behaviour of Geomaterials. International Centre for Mechanical Sciences, 1994, vol. 350. Springer, Vienna. DOI: 10.1007/ 978-3-7091-2710-0_3.

33. Günther R.-M., Salzer K., Popp T., Lüdeling C. Steady-state creep of rock salt: Improved approaches for lab determination and modelling. Rock Mechanics and Rock Engineering. 2015, vol. 48, no. 6, pp. 2603—2613. DOI: 10.1007/s00603-015-0839-2.

34. Minkley W., Mühlbauer J. Constitutive models to describe the mechanical behavior of salt rocks and the imbedded weakness planes. The Mechanical Behavior of Salt—Understanding of THMC Processes in Salt. CRC Press, 2017, pp. 119—127.

35. Belyakov N. A., Belikov A. A. Prediction of the integrity of the water-protective stratum at the Verkhnekamskoye potash ore deposit. MIAB. Mining Inf. Anal. Bull. 2022, no. 6-2, pp. 33—46. [In Russ]. DOI: 10.25018/0236_1493_2022_62_0_33.

36. Desai C. S., Varadarajan A. A constitutive model for quasi-static behavior of rock salt. Journal of Geophysical Research. 1987, vol. 92, no. B11, pp. 11445—11456. DOI: 10.1029/ JB092iB11p11445.

37. Desai C. S., Zhang D. Viscoplastic model for geologic materials with generalized flow rule. International Journal for Numerical and Analytical Methods in Geomechanics. 1987, vol. 11, no. 6, pp. 603—620. DOI: 10.1002/nag.1610110606.

38. Desai C. S., Salami M. R. A constitutive model and associated testing for soft rock. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts. 1987, vol. 24, no. 5, pp. 299—307. DOI: 10.1016/0148-9062(87)90866-7.

39. Konstantinova S. A., Aptukov V. N. Nekotorye zadachi mekhaniki deformirovaniya i razrusheniya solyanykh porod [Some problems of deformation and fracture mechanics of salt rocks], Novosibirsk, Nauka, 2013, 191 p.

40. Belyakov N., Smirnova O., Alekseev A., Tan H. Numerical simulation of the mechanical behavior of fiber-reinforced cement composites subjected dynamic loading. Applied Sciences. 2021, vol. 11, no. 3, article 1112. DOI: 10.3390/app11031112.

41. Urai J. L., Spiers C. J. The effect of grain boundary water on deformation mechanisms and rheology of rocksalt during long-term deformation. The Mechanical Behavior of Salt — Understanding of THMC Processes in Salt. CRC Press, 2017, pp. 149—158. DOI: 10.1201/ 9781315106502-17.

42. Quey R., Dawson P. R., Barbe F. Large-scale 3D random polycrystals for the finite element method: Generation, meshing and remeshing. Computer Methods in Applied Mechanics and Engineering. 2011, vol. 200, no. 17—20, pp. 1729—1745. DOI: 10.1016/j.cma.2011.01.002.

43. Kashnikov Yu. A., Ermashov A. O., Efimov A. A. Geological and geomechanical model of the Verkhnekamsk potash deposit site. Journal of Mining Institute. 2019, vol. 237, pp. 259—267. [In Russ]. DOI: 10.31897/pmi.2019.3.259.

44. Karasev M. A., Buslova M. A., Vil'ner M. A., Nguen T. T. Method for predicting the stress-strain state of the vertical shaft lining at the drift landing section in saliferous rocks. Journal of Mining Institute. 2019, vol. 240, pp. 628—637. [In Russ]. DOI: 10.31897/pmi.2019.6.628.

45. Komolov V., Belikov A., Demenkov P. Research on load-bearing constructions behavior during pit excavation under «Slurry Wall» protection. Technological Advancements in Construction. 2022, vol. 180, pp. 313—323. DOI: 10.1007/978-3-030-83917-8_29.